Wow I can sense some deep hatred for Alexstrasza there 
Take a deep breath and relax! It’s really not as bad as you are describing things.
First of all, Handlock plays a 8/8 on 4 mana, Gala Shaman can play 2 8/8 on 7 mana, Rogue can have a 8/8 on 3 mana or 22/22 on 7 mana and this list goes on and on, so I can’t really agree on your argument 9 mana 8/8 is that big of a swing turn as you describing it.
About the comparison with Pyroblast, that’s a mage spell and Alex is neutral that you can put in your own deck as well. Pyro always applys 10 dmg and can even kill you. Alexstrasza never kills you, because it can’t reduce your HP below 15… thats a huge difference!
Reading your post you get the feeling a 9 mana 8/8 is the most broken thing in the game when it sometimes also reduces your HP from 25 to 15 functioning as a ‘pyroblast’, but thats very situational and often you just die yourself if you just play a 9 mana 8/8 and do nothing else.
You were talking a lot about playing competitive vs. playing for fun, but what does that make for a difference? Hearthstone is a game that’s won by reducing your opponents HP from 30 to 0. That’s the rules, I didn’t make them it is just how the game works and there is different strategies to get there. The first thing a new player would try is to build an aggressive Facehunter to try to get the opponent to 0 asap. Then he might realize some opponents have too much heal and the face strategy doesn’t work often enough and that’s where you start to develop and discover new strategies, however the rules stay the same, decks that are more efficient reducing HP from 30 to 0 are stronger than decks running low synergy gameplans that want to do something ‘fun’ instead.
What I am trying to say it is not about after how many turns I personally want the game to finish, Blizzard made it 30 HP and ending the game when one has 0 HP and there is Facehunter strategies that accomplish that around turn 6.
So I really don’t get your argument. The way the game is designed, with 30 HP total and the point of the game being to reduce your opponents life total to 0 HP, I think it is quite amazing there is sometimes games lasting for 30+turns. Average is probably 10-12 turns I’d guess.
Alexstrasza is pretty much a key card for control decks to formulate a win condition and being able to convert the “controlling” into a victory. Without Alex, Warrior would just armor up, but never deal enough dmg to ever win the game.
So if you run aggro decks, you basically never come to the point to play alex yourself or seeing your opponent play it, game is over long time before. As midrange deck, you probably don’t run Alex and you are aware you have to beat the control deck rather quickly, before the control deck can consolidate and in Control mirrors, well you have to be the smarter player to win these…
So again, I really think Alex is fitting in very specific kind of decks and doing a great job there and in your own deckbuilding you have to acknowledge the existence of such decks and formulate a win strategy beforehand how to beat control decks. If you don’t design your decks to do so, yeah I guess Alexstrasza can be annoying, but thats not because Alex is bad design, but thats because you didn’t realize how the game functions and play non-efficient decks.
Like what you are describing is like playing chess and move your knight 5 times in a row, because you claim you don’t like to play competitive and complaining that the other guy always check mates you after 6 turns. Maybe learn from that and stop moving your knight 5 times in a row and start playing more efficient in terms of how the entire game is designed. You can still have fun and follow some basic chess rules the same time. Try to use that knowledge when playing hearthstone.